G := sub<Sym(100)|(1, 7)(2, 79)(3, 69)(4, 59)(5, 82)(6, 73)(8, 58)(9, 92)(10, 68)(11, 53)(12, 72)(13, 78)(14, 77)(15, 29)(16, 61)(17, 56)(18, 67)(19, 95)(20, 60)(21, 76)(22, 48)(23, 91)(24, 71)(25, 75)(26, 28)(27, 87)(30, 100)(31, 93)(32, 51)(33,85)(34, 39)(35, 43)(36, 49)(37, 65)(38, 89)(40, 96)(41, 62)(42, 44)(45, 86)(46, 94)(47, 50)(52, 97)(54, 84)(55, 74)(57, 64)(63, 80)(66, 88)(70, 98)(81, 90)(83, 99),(1, 43)(2, 58)(3, 16)(4, 61)(5, 31)(6, 9)(7, 42)(8, 98)(10, 29)(11, 52)(12, 75)(13, 99)(14, 46)(15, 36)(17, 18)(19, 49)(20, 69)(21, 66)(22, 68)(23, 39)(24, 48)(25, 85)(26, 96)(27, 73)(28, 77)(30, 60)(32, 90)(33, 34)(35, 97)(37, 62)(38, 79)(40, 50)(41, 91)(44, 93)(45, 95)(47, 57)(51, 56)(53, 82)(54, 89)(55, 74)(59, 76)(63, 64)(65, 72)(67, 87)(70, 83)(71, 86)(78, 84)(80, 94)(81, 92)(88, 100),(1, 4)(2, 47)(3, 21)(5, 84)(6, 74)(7, 73)(8, 38)(9, 20)(10, 97)(11, 87)(12, 86)(13, 18)(14, 77)(15, 60)(16, 57)(17, 52)(19, 55)(22, 83)(23, 51)(24, 75)(25, 65)(26, 62)(27, 31)(28, 71)(29, 56)(30, 46)(32, 99)(33, 34)(35, 100)(36,48)(37, 78)(39, 44)(40, 79)(41, 67)(42, 89)(43, 53)(45, 59)(49, 98)(50, 69)(54, 96)(58, 64)(61, 85)(63, 70)(66, 68)(72, 95)(76, 82)(80, 91)(81, 93)(88, 92)(90, 94)>;

involutions :=

[
[
    G!(1, 7)(2, 79)(3, 69)(4, 59)(5, 82)(6, 73)(8, 58)(9, 92)(10, 68)(11, 53)(12, 72)(13, 78)(14, 77)(15, 29)(16, 61)(17, 
        56)(18, 67)(19, 95)(20, 60)(21, 76)(22, 48)(23, 91)(24, 71)(25, 75)(26, 28)(27, 87)(30, 100)(31, 93)(32, 51)(33,
        85)(34, 39)(35, 43)(36, 49)(37, 65)(38, 89)(40, 96)(41, 62)(42, 44)(45, 86)(46, 94)(47, 50)(52, 97)(54, 84)(55, 
        74)(57, 64)(63, 80)(66, 88)(70, 98)(81, 90)(83, 99),
    G!(1, 43)(2, 58)(3, 16)(4, 61)(5, 31)(6, 9)(7, 42)(8, 98)(10, 29)(11, 52)(12, 75)(13, 99)(14, 46)(15, 36)(17, 18)(19, 
        49)(20, 69)(21, 66)(22, 68)(23, 39)(24, 48)(25, 85)(26, 96)(27, 73)(28, 77)(30, 60)(32, 90)(33, 34)(35, 97)(37, 
        62)(38, 79)(40, 50)(41, 91)(44, 93)(45, 95)(47, 57)(51, 56)(53, 82)(54, 89)(55, 74)(59, 76)(63, 64)(65, 72)(67, 
        87)(70, 83)(71, 86)(78, 84)(80, 94)(81, 92)(88, 100),
    G!(1, 4)(2, 47)(3, 21)(5, 84)(6, 74)(7, 73)(8, 38)(9, 20)(10, 97)(11, 87)(12, 86)(13, 18)(14, 77)(15, 60)(16, 57)(17, 
        52)(19, 55)(22, 83)(23, 51)(24, 75)(25, 65)(26, 62)(27, 31)(28, 71)(29, 56)(30, 46)(32, 99)(33, 34)(35, 100)(36,
        48)(37, 78)(39, 44)(40, 79)(41, 67)(42, 89)(43, 53)(45, 59)(49, 98)(50, 69)(54, 96)(58, 64)(61, 85)(63, 70)(66, 
        68)(72, 95)(76, 82)(80, 91)(81, 93)(88, 92)(90, 94)
]
,
[
    G!(1, 58)(2, 78)(3, 21)(4, 64)(5, 69)(6, 74)(7, 39)(8, 34)(9, 13)(10, 97)(11, 12)(14, 77)(15, 60)(16, 53)(17, 28)(18, 
        20)(19, 89)(22, 83)(23, 36)(24, 68)(25, 96)(26, 62)(27, 30)(29, 67)(31, 46)(32, 99)(33, 38)(35, 59)(37, 47)(40, 
        88)(41, 56)(42, 55)(43, 57)(44, 73)(45, 100)(48, 51)(49, 98)(50, 84)(52, 71)(54, 65)(61, 72)(63, 80)(66, 75)(70,
        91)(76, 82)(79, 92)(81, 94)(85, 95)(86, 87)(90, 93),
    G!(1, 7)(2, 22)(3, 60)(4, 30)(5, 86)(6, 32)(8, 31)(9, 81)(10, 42)(11, 53)(12, 17)(13, 78)(14, 57)(15, 35)(16, 61)(18, 
        96)(19, 97)(20, 69)(21, 76)(23, 94)(24, 70)(25, 28)(26, 75)(27, 65)(29, 43)(33, 80)(34, 39)(36, 49)(37, 87)(38, 
        83)(40, 67)(41, 47)(44, 68)(45, 82)(46, 91)(48, 79)(50, 62)(51, 73)(52, 95)(54, 84)(55, 74)(56, 72)(58, 93)(59, 
        100)(63, 85)(64, 77)(66, 88)(71, 98)(89, 99)(90, 92),
    G!(1, 87)(2, 76)(3, 45)(4, 61)(5, 31)(6, 60)(7, 54)(8, 29)(9, 30)(10, 98)(11, 85)(12, 97)(13, 65)(14, 46)(15, 79)(16, 
        95)(17, 18)(19, 71)(20, 77)(21, 64)(22, 68)(23, 100)(24, 51)(25, 52)(26, 96)(27, 37)(28, 69)(32, 57)(33, 34)(35,
        75)(36, 38)(39, 88)(40, 74)(41, 91)(42, 89)(43, 67)(44, 81)(47, 90)(48, 56)(49, 86)(50, 55)(53, 80)(58, 59)(62, 
        73)(63, 66)(70, 83)(72, 99)(78, 84)(82, 94)(92, 93)
]
,
[
    G!(1, 36)(2, 22)(3, 31)(4, 74)(5, 16)(6, 75)(7, 17)(8, 70)(9, 12)(10, 38)(11, 19)(13, 85)(14, 72)(15, 43)(18, 42)(20, 
        26)(21, 92)(23, 97)(24, 33)(25, 99)(27, 57)(28, 37)(29, 79)(30, 40)(32, 56)(34, 48)(35, 39)(41, 53)(44, 59)(45, 
        71)(46, 65)(47, 73)(49, 52)(50, 60)(51, 90)(54, 67)(55, 61)(58, 68)(62, 77)(63, 94)(64, 80)(66, 81)(69, 96)(76, 
        93)(78, 100)(82, 91)(83, 98)(84, 88)(86, 95)(87, 89),
    G!(1, 67)(2, 76)(3, 57)(4, 41)(5, 81)(6, 24)(7, 38)(8, 73)(9, 69)(10, 80)(11, 30)(12, 44)(13, 60)(14, 59)(15, 18)(16, 
        21)(17, 85)(19, 48)(20, 50)(22, 27)(23, 79)(25, 72)(26, 33)(28, 68)(29, 70)(31, 83)(32, 54)(34, 62)(35, 88)(36, 
        55)(37, 94)(39, 86)(40, 51)(42, 49)(43, 58)(45, 77)(46, 87)(47, 82)(52, 61)(53, 64)(56, 63)(65, 95)(66, 71)(74, 
        75)(78, 90)(84, 93)(89, 98)(91, 97)(92, 100)(96, 99),
    G!(1, 10)(2, 78)(3, 43)(4, 33)(5, 95)(6, 56)(7, 68)(8, 100)(9, 48)(11, 60)(12, 94)(13, 79)(14, 36)(15, 62)(16, 63)(17,
        73)(18, 50)(19, 82)(20, 53)(21, 32)(22, 92)(23, 57)(24, 25)(26, 52)(27, 93)(28, 97)(29, 41)(30, 58)(31, 87)(34, 
        86)(35, 69)(37, 74)(38, 42)(39, 45)(40, 54)(44, 89)(46, 72)(47, 67)(49, 77)(51, 76)(55, 65)(59, 85)(61, 80)(64, 
        91)(66, 98)(70, 88)(71, 75)(81, 99)(83, 90)(84, 96)
]
,
[
    G!(1, 7)(2, 62)(3, 37)(4, 28)(5, 58)(6, 63)(8, 33)(9, 27)(10, 14)(11, 17)(12, 34)(13, 23)(15, 68)(16, 52)(18, 100)(19,
        87)(20, 49)(21, 86)(22, 65)(24, 43)(25, 57)(26, 70)(29, 59)(30, 42)(31, 81)(32, 60)(35, 71)(36, 93)(38, 64)(39, 
        84)(40, 83)(41, 61)(44, 89)(45, 97)(46, 78)(47, 73)(48, 92)(50, 85)(51, 74)(53, 66)(54, 72)(55, 90)(56, 88)(67, 
        75)(69, 95)(76, 79)(77, 98)(80, 82)(91, 94)(96, 99),
    G!(1, 82)(2, 36)(3, 49)(4, 90)(5, 18)(6, 22)(7, 88)(8, 21)(9, 60)(10, 27)(11, 65)(12, 14)(13, 20)(15, 26)(16, 55)(17, 
        97)(19, 62)(23, 79)(24, 76)(25, 89)(28, 38)(29, 86)(30, 68)(31, 35)(32, 81)(33, 92)(34, 100)(37, 43)(39, 69)(40,
        71)(41, 91)(42, 61)(44, 51)(45, 67)(46, 83)(47, 99)(48, 54)(50, 64)(52, 96)(53, 74)(56, 85)(57, 77)(58, 78)(59, 
        93)(63, 94)(66, 98)(70, 75)(72, 84)(73, 80)(87, 95),
    G!(1, 49)(2, 4)(3, 86)(5, 16)(6, 21)(7, 44)(8, 95)(9, 69)(10, 99)(11, 97)(12, 74)(13, 41)(14, 27)(15, 60)(17, 24)(18, 
        34)(19, 64)(20, 23)(22, 47)(25, 56)(26, 80)(28, 35)(29, 65)(30, 58)(31, 91)(32, 87)(33, 96)(36, 85)(37, 90)(38, 
        50)(39, 76)(40, 55)(42, 68)(43, 72)(45, 78)(46, 89)(48, 67)(51, 53)(52, 98)(54, 61)(57, 84)(59, 70)(62, 92)(63, 
        71)(66, 79)(73, 82)(75, 83)(77, 93)(81, 88)(94, 100)
]
,
[
    G!(1, 73)(2, 26)(3, 32)(4, 65)(5, 11)(6, 21)(7, 17)(8, 96)(9, 84)(10, 55)(12, 34)(13, 30)(14, 50)(15, 42)(16, 46)(18, 
        28)(19, 82)(20, 93)(22, 36)(23, 63)(24, 90)(25, 79)(27, 52)(29, 80)(31, 41)(33, 81)(35, 74)(37, 44)(38, 98)(39, 
        68)(40, 78)(43, 85)(45, 99)(47, 72)(48, 56)(49, 64)(51, 87)(53, 86)(54, 94)(57, 62)(58, 91)(59, 100)(60, 76)(61,
        70)(66, 67)(69, 92)(71, 77)(75, 83)(88, 95)(89, 97),
    G!(1, 80)(2, 49)(3, 26)(4, 76)(5, 29)(6, 96)(7, 78)(8, 22)(9, 70)(10, 19)(11, 63)(12, 14)(13, 85)(15, 32)(16, 64)(17, 
        99)(18, 72)(20, 43)(21, 86)(23, 41)(24, 62)(25, 31)(27, 37)(28, 67)(30, 69)(33, 53)(34, 87)(35, 59)(36, 40)(38, 
        74)(39, 84)(42, 90)(44, 83)(45, 92)(46, 82)(47, 60)(48, 94)(50, 61)(51, 52)(54, 88)(55, 95)(56, 100)(57, 98)(58,
        71)(65, 66)(68, 73)(75, 79)(77, 81)(89, 93)(91, 97),
    G!(1, 88)(2, 61)(3, 44)(4, 8)(5, 24)(6, 13)(7, 79)(9, 59)(10, 75)(11, 60)(12, 74)(14, 56)(15, 30)(16, 40)(17, 69)(18, 
        77)(19, 29)(20, 41)(21, 94)(22, 91)(23, 82)(25, 33)(26, 38)(27, 35)(28, 68)(31, 70)(32, 71)(34, 64)(36, 45)(37, 
        87)(39, 98)(42, 67)(43, 99)(46, 83)(47, 95)(48, 51)(49, 54)(50, 96)(52, 100)(53, 85)(55, 81)(57, 76)(58, 86)(62,
        78)(63, 90)(65, 93)(66, 97)(72, 84)(73, 89)(80, 92)
]
,
[
    G!(1, 98)(2, 54)(3, 47)(4, 34)(5, 96)(6, 79)(7, 38)(8, 48)(9, 71)(10, 51)(11, 43)(12, 57)(13, 52)(14, 22)(15, 89)(16, 
        55)(17, 26)(18, 70)(19, 58)(20, 39)(21, 74)(23, 27)(24, 99)(25, 87)(28, 100)(29, 67)(30, 36)(31, 78)(32, 95)(33,
        91)(35, 90)(37, 92)(40, 45)(41, 46)(42, 59)(44, 73)(49, 60)(50, 63)(53, 93)(56, 65)(61, 68)(62, 88)(64, 97)(66, 
        75)(69, 82)(72, 85)(76, 86)(77, 80)(81, 94)(83, 84),
    G!(1, 63)(2, 70)(3, 10)(4, 73)(5, 86)(6, 15)(7, 61)(8, 65)(9, 81)(11, 50)(12, 40)(13, 89)(14, 62)(16, 41)(17, 67)(18, 
        90)(19, 27)(20, 55)(21, 83)(22, 32)(23, 94)(24, 35)(25, 88)(26, 82)(28, 75)(29, 43)(30, 51)(31, 36)(33, 96)(34, 
        84)(37, 80)(38, 69)(39, 58)(42, 46)(44, 95)(45, 66)(47, 85)(48, 93)(49, 97)(52, 68)(53, 100)(54, 79)(56, 71)(57,
        59)(60, 77)(64, 91)(72, 78)(74, 76)(87, 92)(98, 99),
    G!(1, 39)(2, 3)(4, 32)(5, 65)(6, 80)(7, 55)(8, 12)(9, 30)(10, 92)(11, 61)(13, 49)(14, 83)(15, 96)(16, 66)(17, 38)(18, 
        27)(19, 86)(20, 48)(21, 84)(22, 75)(23, 62)(24, 57)(25, 94)(26, 91)(28, 79)(29, 97)(31, 71)(33, 42)(34, 78)(35, 
        95)(36, 74)(37, 40)(41, 69)(43, 67)(44, 81)(45, 87)(46, 47)(50, 60)(51, 85)(52, 82)(53, 54)(56, 93)(58, 70)(59, 
        90)(63, 68)(64, 89)(72, 99)(73, 100)(76, 88)(77, 98)
]

];

geometries := [* *];


for i in [1..#involutions] do
	G1 := sub<G|involutions[i][2],involutions[i][3]>;
	G2 := sub<G|involutions[i][1],involutions[i][3]>;
	G3 := sub<G|involutions[i][1],involutions[i][2]>;
	Append(~geometries,CosetGeometry(G,{G1,G2,G3}));
end for;